Laws of Motion

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2 : 1. After disintegration they will move :

1. in opposite directions with speed in the ratio of 1 : 2 respectively.
2. in the same direction with same speed.
3. in opposite directions with speed in the ratio of 2 : 1 respectively.
4. in opposite directions with the same speed.

A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45 with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and g = 10 m/s2) [figure]

1. 1 N
2. 10 N
3. 10 2 N
4. 110 2 N

A stationary particle breaks into two parts of masses mA and mB which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB : KA) is :

1. vB : vA
2. 1 : 1
3. mB vB : mA vA
4. mB : mA

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:

1. 150 N
2. 3 N
3. 30 N
4. 300 N

A given object takes n times the time to slide down 45 rough inclined plane as it takes the time to slide down an identical perfectly smooth 45 inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

1. 1 - 1n2
2. 1 - 1n2
3. 1 - n2
4. 1 - n2

A circular table is rotating with an angular velocity of rad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x 2 m/s, where the value of x is . [figure]

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2 > m1). If the acceleration of the system is g 2, then the ratio of the masses m1m2 is:

1. 1 + 5 5 - 1
2. 3 + 1 2 - 1
3. 2 - 1 2 + 1
4. 1 + 5 2 - 1

A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30 . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: (g = 10 m/s2, 3 = 1.73 )

1. 51.4 m/s
2. 102.8 m/s
3. 70.4 m/s
4. 264 m/s

A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2) :

1. 300 N
2. 100 N
3. 150 N
4. 200 N

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 ms-2. The action force of the system on the floor is equal to :

1. 297 N
2. 291 N
3. 196 N
4. 294 N